The magnetic susceptibility of a sample describes the relation between an applied magnetic field H and the magnetization M induced in the sample by the magnetic field. The differential volume susceptibility .chi. is defined as ##EQU1## Since the applied magnetic field H and the magnetization M (magnetic moment per unit volume) are vectors, the susceptibility .chi. is most generally a second-rank tensor, especially for anisotropic materials. For diamagnetic, paramagnetic or antiferromagnetic material, the magnetization M is linearly related to the applied magnetic field H as EQU M=.chi..multidot.H, (2)
where the largest components of the susceptibility tensor .chi. are typically on the order of 10.sup.-5. For such materials, the susceptibility tensor .chi. does not depend on the applied magnetic field H and the susceptibility has the same value as the differential susceptibility.
Magnetometers can be used to measure susceptibility by applying a known magnetic field to a sample and measuring the induced magnetic moment. They can also be used to measure differential susceptibility.
In a vibrating sample magnetometer, the sample is mounted on a support which is vibrated in a known magnetic field, thereby electromagnetically inducing voltage in a detection coil. See, S. Foner, "Versatile and Sensitive Vibrating-Sample Magnetometer," Rev. Sci. Instrum. 30, 548 (1959). The amplitude of the induced signal is considered to be a measure of the sample's magnetic moment and, therefore, susceptibility. As such a system measures magnetization by the effect of the sample on the current in a detection coil, it is limited in sensitivity by the noise and other limiting characteristics of the coil and its associated electronics. Such a system does not become more sensitive as the size of the specimen decreases and is not as effective as the size of the specimen decreases.
The frequency of vibration in a vibrating sample magnetometer is determined by the driving system and is not affected by properties of the sample. Furthermore, the test sample is mounted on a support, which may have a magnetization of its own, and thus a nulling procedure is used to subtract this effect. As the sensitivity of the vibrating sample magnetometer cannot readily be calculated a priori, such a system is typically calibrated against a known standard.
A vibrating sample magnetometer does not directly measure anisotropic aspects of susceptibility. In order to determine the difference between two components of susceptibility, the two components are first measured and then compared. Since the difference may be orders of magnitude smaller than the components themselves, such an indirect technique may introduce significant errors in measuring anisotropic aspects of susceptibility.
Force magnetometers measure a sample's magnetic moment by measuring the magnetic force exerted on the sample by an applied nonhomogeneous magnetic field. There are difficulties with producing the optimum nonhomogeneous magnetic field. One type of force magnetometer is a vibrating reed magnetometer, in which the sample is mounted on a flexible support. The sample mounted on the support is driven by an ac magnetic field at the flexible support's mechanical resonant frequency, and the flexible support provides a restoring mechanical force. The amplitude of vibration is considered proportional to the sample's magnetic moment. See, H. Zijlstra, "A Vibrating Reed Magnetometer for Microscopic Particles," Rev. Sci. Instrum. 41, 1241 (1970); W. Roos, "High Sensitivity Vibrating Reed Magnetometer," Rev Sci. Instrum. 51(5), 612 (1980). This technique has the same shortcomings as those discussed above for the vibrating sample magnetometer. It does not become more sensitive as the size of the specimen decreases and is not as effective as the size of the specimen decreases. It does not directly measure anisotropic aspects of susceptibility. Furthermore, because the vibrating reed magnetometer uses an external support which might affect the magnetization results, a nulling or subtraction procedure is used with such a system.
Vibrating reed experiments which measure changes in the resonant frequency of flexural resonance have been used to study the dynamics of superconductors. However, such experiments are related to flux line pinning and are not sensitive to anisotropic aspects of the sample's magnetic susceptibility. Such experiments do not measure anisotropic aspects of a sample's inherent magnetic susceptibility.